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## Official Guide Explanation:Data Sufficiency #114

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 114
Page: 161
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Quadrilaterals >
Category 2: Geometry > Triangles > Multiple figures

Explanation: To find the area, you need the length and the width. Statement (1) is insufficient: you'd need another equation with l and w to solve for the value of each. Statement (2) is also insufficient. Since d is the hypotenuse of a right triangle with sides l and w, you can create this equation:

l2 + w2 = d2

l2 + w2 = 20

Taken together, the statements are sufficient. Given two equations and two variables, even with the squares making the equations non - linear, it's likely you can solve for the area. However, it's worth making sure:

l + w = 6

(l + w)2 = 36

l2 + 2lw + w2 = 36

Now, compare that to the equation from (2):

l2 + w2 = 20

Subtract that equation from the one that preceded it, resulting in:

2lw = 16

lw = 8

That's the area of the rectangle, so the correct choice is (C).

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